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This paper aims to analyze the accuracy of the single and two-phase numerical methods for calculation of ferrofluid convective heat transfer in the presence of a magnetic field. The findings of current study are compared with previous single-phase numerical results and experimental data. Accordingly, the effect of various parameters including nanoparticles concentration, Reynolds number and magnetic field strength on the performance of the single and two-phase models are evaluated.

A two-phase mixture numerical study is carried out to investigate the influence of four U-shaped electromagnets on the hydrodynamic and thermal characteristics of Fe₃O₄/Water ferrofluid flowing inside a heated channel.

It is observed that the applied external magnetic field signifies the convective heat transfer from the channel surface, despite local reduction at a few locations. The maximum heat transfer enhancement is predicted as 23% and 25% using single and two-phase models, respectively. The difference between the results of the two models is mainly attributed to the slip velocity effect which is accounted for in the two-phase model. The magnetic field gradient leads to a significant increase in the slip velocity which in turn causes a slight difference in velocity and temperature profiles obtained by the single and two-phase models in the magnetic field region. According to percentage error calculation, the two-phase method is generally more accurate than the single-phase method. However, the percentage error of both models improves by decreasing either magnetic field intensity or Reynolds number.

For the first time in the literature, to the best of the authors’ knowledge, the current work analyzes the accuracy of the single and two phase numerical methods for calculation of ferrofluid convective heat transfer in the presence of a magnetic field.

To analyze two‐phase flow in micro‐channel heat exchangers used for high flux micro‐electronics cooling and to obtain performance parameters such as thermal resistance, pressure drop, etc. Both uniform and non‐uniform micro‐channel base heat fluxes are considered.

Energy balance equations are developed for two‐phase flow in micro‐channels and are solved using the finite element method (FEM). A unique ten noded element is used for the channel descritization. The formulation also automatically takes care of single‐phase flow in the micro‐channel.

Micro‐channel wall temperature distribution, thermal resistance and the pressure drop for various uniform micro‐channel base heat fluxes are obtained, both for single‐ and two‐phase flows in the micro‐channel. Results are compared against data available in the literature. The wall temperature distribution for a particular case of non‐uniform base heat flux is also obtained.

The analysis is done for a single micro‐channel and the effects of multiple or stacked channels are not considered. The analysis needs to be carried out for higher heat fluxes and the validity of the correlation needs to be ascertained through experimentation. Effects of flow mal‐distribution in multiple channels, etc. need to be considered.

The role of two‐phase flow in micro‐channels for high flux micro‐electronics cooling in reducing the thermal resistance is demonstrated. The formulation is very useful for the thermal design and management of microchannels with both single‐ and two‐phase flows for either uniform or non‐uniform base heat flux.

A simple approach to accurately determine the thermal resistance in micro‐channels with two‐phase flow, for both uniform and non‐uniform base heat fluxes is the originality of the paper.

This paper aims to present a financial valuation framework based on the real options theory to evaluate investments in toll road projects delivered under the two‐phase development plan.

The approach is based on applying the real options theory to evaluate investments in toll road projects. In particular, the risk‐neutral valuation method is used for pricing flexibility embedded in the two‐phase development plan. Risk‐neutral binomial lattice is used to model traffic uncertainty and to find the optimal time for the toll road expansion. Probabilistic life cycle cost and revenue analysis is conducted to characterize the investor's financial risk profile and determine the flexibility value of the expansion option.

The flexible, two‐phase development plan can improve the investor's financial risk profile in the toll road project through limiting the downside risk of overinvestment (i.e. decreasing the probability of investment loss) and increasing the expected investment value in a highway project.

Private and public sectors can benefit from this valuation framework and use tax dollars and users' fees effectively through avoiding overinvestment in toll road projects.

The framework consists of several integrated features, which distinguish it from existing investment valuation models. The risk‐neutral valuation method for pricing flexibility embedded in the two‐phase development plan is applied. This real options framework is capable of characterizing traffic boundary, at which it is optimal for the investor to expand the toll road. Further, this framework provides the likelihood distribution of when the investor may expand the toll road.

A mathematical model is developed for the description of the thermohydraulics of the two‐phase flow phenomenon in a vertical pipe. Using an additional momentum equation for the slip velocity, it is shown that the computation of slip and pressure drop from the model equations is possible without the use of any external correlations. The finite element method is used to solve the governing equations. The predictions for a steam‐water two‐phase flow in vertical upflow with constant wall heat flux agree well with experimental results and with widely used correlations.

A consistent implementation of the general computational framework of unified second-order time accurate integrators via the well-known GSSSS framework in conjunction with the traditional Finite Difference Method is presented to improve the numerical simulations of reactive two-phase flows.

In the present paper, the phase interaction evaluation in the present implementation of the reactive two-phase flows has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process for solving the two phase flow dynamics with reactions.

Numerical examples, including the classical Sod shock tube problem and a reactive two-phase flow problem, are exploited to validate the proposed time integration framework and families of algorithms consistently to second order in time accuracy; this is in contrast to the traditional practices which only seem to obtain first-order time accuracy because of the inconsistent time level implementation with respect to the interaction of two phases. The comparisons with the traditional implementation and the advantages of the proposed implementation are given in terms of the improved numerical accuracy in time. The proposed approaches provide a correct numerical simulation implementation to the reactive two-phase flows and can obtain better numerical stability and computational features.

The new algorithmic framework and the consistent time level evaluation extended with the GS4 family encompasses a multitude of past and new schemes and offers a general purpose and unified implementation for fluid dynamics.

In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

An easy‐to‐use numerical model for transient two‐phase pipe flow analyses was developed by applying the split‐coefficient matrix method (SCMM) to a homogeneous equilibrium two‐phase flow model. The basic idea of the SCMM is to split the Jacobian coefficient matrix into two sub‐vectors, each associated with eigenvalues of the same sign. Hence, one‐sided finite difference schemes can accordingly be applied to the sub‐vectors. The present model was validated against experiments. It is numerically stable provided that a criterion is met due to the use of a time explicit format. The satisfactory agreement between the numerical and experimental results indicates that the model may be used as a simple, efficient tool for general engineering analyses of transient two‐phase flow. The advantages of applying SCMM to transient two phase flows are briefly addressed, and it is applicable to systems having real eigenvalues.

The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.

The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.

The method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.

While relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

Investigates the effects of two‐phase instability on finite element (FE) solutions for porous hypoelastic solids saturated with an insterstitial fluid. Demonstrates that two‐phase instability creates definite problems to the FE computations of coupled solid‐fluid systems. The eigenvectors of the tangential finite element matrices which are responsible for problems are not artificial, but are the bifurcating modes of physical solutions. The investigation, although limited to the plane strain undrained compression of hypoelastic models, is relevant to the investigation of the two‐phase instability of other materials and boundary value problems, and may lead towards an explanation for numerical problems in soil liquefaction analysis.

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical oscillations in the region where the gradient is high. This paper aims to improve the ability to capture the complex shock wave during the interior ballistic cycle.

A two-phase flow model is established to describe the complex physical process based on a modified two-fluid theory. The solution of model is obtained including the following key methods: an approximate Riemann solver to construct upwind fluxes, the MUSCL extension to achieve high-order accuracy, a splitting approach to solve source terms, a self-adapting method to expand the computational domain for projectile motion and a control volume conservation method for the moving boundary.

The paper is devoted to applying a high-resolution numerical method to simulate a transient two-phase reactive flow with moving boundary in guns. Several verification tests demonstrate the accuracy and reliability of this approach. Simulation of two-phase reaction flow with a projectile motion in a large-caliber gun shows an excellent agreement between numerical simulation and experimental measurements.

This paper has implications for improving the ability to capture the complex physics phenomena of two-phase flow during interior ballistic cycle and predict the combustion details, such as the flame spreading, the formation of pressure waves and so on.

This approach is reliable as a prediction tool for the understanding of the physical phenomenon and can therefore be used as an assessment tool for future interior ballistics studies.